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Difficulty: Hard
Category: options_pricing
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Topics: barrier_option, down_and_out, reflection_principle, black_scholes, options_pricing
Barrier options are exotic derivatives that become worthless if the underlying asset's price touches a predetermined barrier level. The down-and-out call option is a common variant, particularly in equity and FX markets, where the option is nullified if the underlying price drops to the barrier. Quants price these instruments analytically under the Black-Scholes model using the reflection principle. Task Implement the function barrier_option_down_out_call(S, K, H, r, sigma, T) to calculate the
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